There isn't much to the knife defense, it's a very practical idea, and that is to immediately attack and control the head to prevent further attacks instead of trying to control the knife. When facing a knife, fishing for controlling the arms is too dangerous because you can't control the attacker's balance and prevent continued attacks until after you've already secured the arm. This is what leads to repeated slashes to the arms and torso. The head is far easier to grab, and it's hard to keep attacking with the knife when your head is being twisted and spiked into the ground like football. This video is sort of similar in principle in that there is almost immediate head control: